_1-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update

Abstract

We develop a dictionary learning algorithm by minimizing the _1 distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization of weighted _2 error. We refer to this algorithm as _1-K-SVD, where the dictionary atoms and the corresponding sparse coefficients are simultaneously updated to minimize the _1 objective, resulting in noise-robustness. We demonstrate through experiments that the _1-K-SVD algorithm results in higher atom recovery rate compared with the K-SVD and the robust dictionary learning (RDL) algorithm proposed by Lu et al., both in Gaussian and non-Gaussian noise conditions. We also show that, for fixed values of sparsity, number of dictionary atoms, and data-dimension, the _1-K-SVD algorithm outperforms the K-SVD and RDL algorithms when the training set available is small. We apply the proposed algorithm for denoising natural images corrupted by additive Gaussian and Laplacian noise. The images denoised using _1-K-SVD are observed to have slightly higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise, but the improvement in structural similarity index (SSIM) is significant (approximately 0.1) for lower values of input PSNR, indicating the efficacy of the _1 metric.

Tasks

Reproductions